At lunchtime Tuesday, Dmitri Matheny played at an Episcopal church in Muskegon. The same night, he performed at a pub in Lansing. After a travel day, it was a cabaret in Kalamazoo, a club in Detroit, and a micro-brewery in Douglas.

Perhaps not every musician’s fantasy week in Michigan, but it’s work. And Matheny has learned at the ripe age of 51 that one can’t reject an offer. Not often, anyway.

“I say ‘yes’ to everything,” he said laughing. “It doesn’t always make sense. But I love to play.”

It usually works. Sometimes not. Sometimes more than just sometimes.

How often does he ponder“What was I thinking?”

“Quite often,” he said. “I don’t know how else to live. I’ve been touring since 1995 and most of the jobs that we do are one-nighters.”

That can work in the heart of Michigan. Not near San Francisco where Matheny made his home for 20 years before fleeing the insane cost of living for Washington state.

“The thing about the Bay Area is that you can play Yoshi’s once, maybe twice a year. You can’t play several weeks and come back,” Matheny said. “Just trying to piece together a patchwork of one-nighters, you have to be willing to travel.”

Matheny returns to these parts June 4 for a Sunday gig at the Empress Theatre on behalf of the Vallejo Jazz Society, landing here after two nights at a bistro in Truckee.

As he said, a guy’s got to be willing to travel when you earn a living playing flugelhorn.

“For me, it’s pretty routine,” he said of the road gigs. “I really love it. If I do it right, it ends up being a kind of residency. I have my rhythm section I work with in the Midwest and if I put together a week or two, it becomes an annually-anticipated thing.”

Sure, he said, “there are travel mishaps. Luggage sometimes doesn’t quite catch up to you. And someone may want to mail you a check when I’ll be home in six months. But it beats other things I’ve had to do for a living.”

Though Matheny has seemingly had some kind of music-related employment, it hasn’t always gone well. His last “day job” was director of education for S.F. Jazz.

“I had a desk and an office and there were meetings and memos,” he said. “So it was a ‘real job.’”

But not, apparently, the one he wanted.

“I did my best, but I don’t think I was very good at it,” Matheny said. “The teaching, I enjoyed. But all the administration was not my skill set.”

What he also had — and, looking back, wise to do — were a handful of temp jobs that gave him a handle on the behind-the-scenes of the music industry after he graduated from the Berklee College of Music in Boston.

There were classes that taught about royalties and contract negotiations, “things like that,” Matheny said.

So he took the knowledge to short-lived jobs working for a record company, then a radio station and then for a music publicist. And then he did some grant writing for a museum. All these jobs “that makes it possible for artists and musicians to make a living.”

“It served me well for the things I’m able to do now,” he said.

As for actual performing, Matheny took up trumpet at 9 but gravitated to the flugelhorn at 16.

“I’ve loved the sound of it ever since I first heard it,” he said, grateful for studying 10 years under Art Farmer, a flugelhorn pioneer of sorts who played with Thelonious Monk and Charles Mingus.

“To me, he’s still the greatest in history,” said Matheny, accustomed to explaining exactly what a flugelhorn is.

“When I do shows for kids and tell them it’s a ‘flugelhorn,’ they all giggle,” Matheny said. “They think it’s a made up Dr. Seuss kind of thing. It’s a legitimate instrument.”

Matheny said he’s still learning how to improve, no matter that he’s played it 35 years.

“Playing a soft volume so you can be heard and blend properly with other instruments, over the years, is something I continue to work on,” he said. “And playing behind a singer when you play just enough where it enhances the listening experience.”

Creating the perfect original melody is always the destination, Matheny said.